We analyze the contact network of simulated two-dimensional granular packings in different states of
mechanical equilibrium obtained by tapping. We show that topological descriptors of the contact network
allow one to distinguish steady states of the same mean density obtained with different tap intensities. These equal-density states were recently proven to be distinguishable through the mean force moment tensor. In contrast, geometrical descriptors, such as radial distribution functions, bond order parameters, and Voronoi cell distributions, can hardly discriminate among these states. We find that small-order loops of contacts—the polygons of the network—are especially sensitive probes for the contact structure.
